Advertisements
Advertisements
Question
Find the sum of the following arithmetic series:
`7 + 10 1/2 + 14 + ....... + 84`
Advertisements
Solution
The given arithmetic series is `7 + 10 1/2 + 14 + ....... + 84`
` Here , a = 7 , d = 10 1/2 - 7 = 21/ 2 - 7 = (21-4)/2 = 7/2 and l = 84.`
Let the given series contains n terms. Then,
an = 84
`⇒ 7 + (n-1) xx 7/2 = 84 [ a_n = a + (n-1) d ]`
` ⇒ 7/2 n + 7/2 = 84`
`⇒ 7/2 n = 84 - 7/2 = 161/2`
`⇒ n = 161/7 = 23`
∴ Required sum`= 23/2 xx (7 + 84) [ s_n = n/2 (a+l) ]`
`=23/2 xx 91`
=`2030/2`
`1046 1/2`
APPEARS IN
RELATED QUESTIONS
Find the term t15 of an A.P. : 4, 9, 14, …………..
Find the sum of the following arithmetic series:
(-5)+(-8)+(-11)+...+(-230)
Given Arithmetic Progression 12, 16, 20, 24, . . . Find the 24th term of this progression.
Six year before, the age of mother was equal to the square of her son's age. Three year hence, her age will be thrice the age of her son then. Find the present ages of the mother and son.
Select the correct alternative and write it.
What is the sum of first n natural numbers ?
Select the correct alternative and write it.
If a share is at premium, then -
Find the 23rd term of the following A.P.: 9, 4,-1,-6,-11.
How many multiples of 4 lie between 10 and 205?
Choose the correct alternative answer for the following sub-question
If the third term and fifth term of an A.P. are 13 and 25 respectively, find its 7th term
Find t5 if a = 3 आणि d = −3
If tn = 2n – 5 is the nth term of an A.P., then find its first five terms
The nth term of an A.P. 5, 8, 11, 14, ...... is 68. Find n = ?
If p - 1, p + 3, 3p - 1 are in AP, then p is equal to ______.
Find a and b so that the numbers a, 7, b, 23 are in A.P.
Write the next two terms of the A.P.: `sqrt(27), sqrt(48), sqrt(75)`......
